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Fields
Institute program on the Mathematics of Oceans is to take place in the year
2013 as a part of the initiative for the Mathematics of Planet Earth.

Overview of the Program

Humankind has always had a fascination with the sea, and advances in civilisation
are closely connected with man's enterprises on the oceans. The topic of nonlinear
waves has its origin in the study of surface water waves, which have relevant
applications to both coastal engineering and naval architecture. The study
of global currents in the Earth's oceans is a topic of importance to the question
of climate stability. Finally, statistical descriptions of nonlinear processes,
such as the wave motion of the sea, are similar to models widely used in quantum
field theory and Navier-Stokes turbulence. Furthermore they are currently
in use in sea state weather prediction, for example in the North Atlantic,
and are therefore relevant to the enterprise of shipping and global supply
chains. All of the above topics are associated with major advances in mathematics,
and as well with major open problems of current interest and mathematical
activity.

The purpose of this Fields Institute program is to bring mathematical analysts
and applied mathematicians together, along with practicing ocean scientists,
to discuss the recent points of progress of these two domains. Furthermore,
our goals are to bring these two communities into contact with ocean scientists,
in a venue in which they can articulate the results of their recent progress,
and ideally to understand its importance and/or relevance to genune oceanographic
applications. There are three principal themes for this program:
(1) nonlinear ocean wave dynamics, including extreme wave dynamics
such as rogue waves and tsunamis,
(2) oceanic circulation and ocean-atmosphere interaction, including
global scale phenomena such as the meridional overturning circulation and
currents such as the Gulf Stream, mesoscale processes described by quasi-geostrophic
flows, as well as highly nonlinear submesoscale processes, including their
role in the stability of the earth's climate, and the impact of their variations;
and
(3) wave interactions and turbulence, including statistical descriptions
of ocean wave spectra and its role in predictions of sea state and weather.

The Program will involve cooperation with AARMS, the Bedford Institute of
Oceanography (Dartmouth, NS), and the Institute of Ocean Sciences (Sydney,
BC).

Program Activities

Coxeter Lecture Series

May 7,9,10, 2013 at 3:30 p.m.Vladimir Zakharov,University of ArizonaWind-driven sea as a subject
for theoretical physics

We prove global existence and modified scattering in physical space
for solutions of the one dimensional water wave equation, with smooth,
small and rapidly decaying Cauchy data. The proof relies on the
one hand on the use of the "good unknown" of Alinhac and
normal forms to establish ${L^2}$ estimates. On the other hand,
${L^{\infty}}$ bounds are obtained combining Klainerman vector fields
and semi-classical analysis to deduce from the PDE an ODE allowing
one to get the asymptotics of the solution. (Joint work with Thomas
Alazard).